Find a quadratic model for the sequence with the indicated terms. $a _ { 0 } = 3 , a _ { 1 } = 1 , a _ { 4 } = 31$
A) $a _ { n } = 3 n ^ { 2 } + 3$
B) $a _ { n } = 3 n ^ { 2 } - 5 n + 3$
C) $a _ { n } = 3 n ^ { 2 } - 3 n + 3$
D) $a _ { n } = 3 n ^ { 2 } - 3 n + 5$
E) $a _ { n } = n ^ { 2 } + 5 n + 3$

Question

Quizplus · Accepted Answer

Given the terms $a_0 = 3$, $a_1 = 1$, and $a_4 = 31$, we can substitute these values into the general quadratic model $a_n = an^2 + bn + c$ to solve for $a$, $b$, and $c$. Substituting $n = 0$ gives $c = 3$. Substituting $n = 1$ and $n = 4$ into the model and solving the resulting system of equations yields $a = 3$ and $b = -5$, making the correct model $a_n = 3n^2 - 5n + 3$.

Find a Quadratic Model for the Sequence with the Indicated a0=3,a1=1,a4=31a _ { 0 } = 3 , a _ { 1 } = 1 , a _ { 4 } = 31a0​=3,a1​=1,a4​=31

Find a Quadratic Model for the Sequence with the Indicated $a _ { 0 } = 3 , a _ { 1 } = 1 , a _ { 4 } = 31$